mirror of
https://github.com/irmen/prog8.git
synced 2024-06-26 07:29:32 +00:00
add various math.atan() routines
This commit is contained in:
Irmen de Jong
parent
3de10adac2
commit
c0b398e0ce
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@ -53,7 +53,8 @@ class VarConstantValueTypeAdjuster(private val program: Program, private val err
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}
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if(to==null) {
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if(!range.to.inferType(program).isInteger)
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val toType = range.to.inferType(program)
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if(toType.isKnown && !range.to.inferType(program).isInteger)
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errors.err("range expression to value must be integer", range.to.position)
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} else if(to-to.toInt()>0) {
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errors.err("range expression to value must be integer", range.to.position)
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@ -95,4 +95,293 @@ _sinecosR8 .char trunc(127.0 * sin(range(180+45) * rad(360.0/180.0)))
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rts
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}}
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}
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sub atan_coarse_sgn(byte x1, byte y1, byte x2, byte y2) -> ubyte {
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; From a pair of signed coordinates around the origin, calculate discrete direction between 0 and 23 into A.
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cx16.r0L = 3 ; quadrant
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cx16.r1sL = x2-x1 ; xdelta
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if_neg {
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cx16.r0L--
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cx16.r1sL = -cx16.r1sL
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}
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cx16.r2sL = y2-y1 ; ydelta
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if_neg {
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cx16.r0L-=2
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cx16.r2sL = -cx16.r2sL
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}
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return atan_coarse_qd(cx16.r0L, cx16.r1L, cx16.r2L)
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}
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sub atan_coarse(ubyte x1, ubyte y1, ubyte x2, ubyte y2) -> ubyte {
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; From a pair of positive coordinates, calculate discrete direction between 0 and 23 into A.
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cx16.r0L = 3 ; quadrant
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if x2>=x1 {
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cx16.r1L = x2-x1
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} else {
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cx16.r1L = x1-x2
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cx16.r0L--
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}
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if y2>=y1 {
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cx16.r2L = y2-y1
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} else {
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cx16.r2L = y1-y2
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cx16.r0L -= 2
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}
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return atan_coarse_qd(cx16.r0L, cx16.r1L, cx16.r2L)
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}
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asmsub atan_coarse_qd(ubyte quadrant @A, ubyte xdelta @X, ubyte ydelta @Y) -> ubyte @A {
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;Arctan https://github.com/dustmop/arctan24
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; From a pair of X/Y deltas (both >=0), and quadrant 0-3, calculate discrete direction between 0 and 23 into A.
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; .reg:a @in quadrant Number 0 to 3.
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; .reg:x @in x_delta Delta for x direction.
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; .reg:y @in y_delta Delta for y direction.
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; Returns A as the direction (0-23).
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%asm {{
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x_delta = cx16.r0L
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y_delta = cx16.r1L
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quadrant = cx16.r2L
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half_value = cx16.r3L
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region_number = cx16.r4L
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small = cx16.r5L
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large = cx16.r5H
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sta quadrant
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sty y_delta
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stx x_delta
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cpx y_delta
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bcs _XGreaterOrEqualY
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_XLessY:
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lda #16
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sta region_number
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stx small
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sty large
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bne _DetermineRegion
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_XGreaterOrEqualY:
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lda #0
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sta region_number
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stx large
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sty small
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_DetermineRegion:
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; set A = small * 2.5
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lda small
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lsr a
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sta half_value
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lda small
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asl a
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bcs _SmallerQuotient
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clc
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adc half_value
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bcs _SmallerQuotient
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cmp large
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bcc _LargerQuotient
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; S * 2.5 > L
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_SmallerQuotient:
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; set A = S * 1.25
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lsr half_value
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lda small
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clc
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adc half_value
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cmp large
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bcc _Region1 ; if S * 1.25 < L then goto Region1 (L / S > 1.25)
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bcs _Region0 ; (L / S < 1.25)
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; S * 2.5 < L
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_LargerQuotient:
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; set A = S * 7.5
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lda small
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asl a
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asl a
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asl a
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bcs _Region2
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sec
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sbc half_value
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cmp large
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bcc _Region3 ; if S * 7.5 < L then goto Region3 (L / S > 7.5)
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jmp _Region2 ; (L / S < 7.5)
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_Region0:
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; L / S < 1.25. d=3,9,15,21
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jmp _LookupResult
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_Region1:
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; 1.25 < L / S < 2.5. d=2,4,8,10,14,16,20,22
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lda region_number
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clc
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adc #4
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sta region_number
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bpl _LookupResult
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_Region2:
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; 2.5 < L / S < 7.5. d=1,5,7,11,13,17,19,23
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lda region_number
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clc
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adc #8
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sta region_number
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bpl _LookupResult
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_Region3:
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; 7.5 < L / S. d=0,6,12,18
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lda region_number
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clc
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adc #12
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sta region_number
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_LookupResult:
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lda quadrant
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clc
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adc region_number
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tax
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lda _quadrant_region_to_direction,x
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rts
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_quadrant_region_to_direction:
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.byte 9, 3,15,21
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.byte 10, 2,14,22
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.byte 11, 1,13,23
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.byte 12, 0,12, 0
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.byte 9, 3,15,21
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.byte 8, 4,16,20
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.byte 7, 5,17,19
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.byte 6, 6,18,18
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}}
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}
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asmsub atan(ubyte x1 @R0, ubyte y1 @R1, ubyte x2 @R2, ubyte y2 @R3) -> ubyte @A {
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;; Calculate the angle, in a 256-degree circle, between two points into A.
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;; The points (x1, y1) and (x2, y2) have to use *unsigned coordinates only* from the positive quadrant in the carthesian plane!
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;; https://www.codebase64.org/doku.php?id=base:8bit_atan2_8-bit_angle
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;; This uses 2 large lookup tables so uses a lot of memory but is super fast.
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%asm {{
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x1 = cx16.r0L
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y1 = cx16.r1L
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x2 = cx16.r2L
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y2 = cx16.r3L
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octant = cx16.r4L ;; temporary zeropage variable
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lda x1
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sbc x2
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bcs *+4
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eor #$ff
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tax
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rol octant
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lda y1
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sbc y2
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bcs *+4
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eor #$ff
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tay
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rol octant
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lda log2_tab,x
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sbc log2_tab,y
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bcc *+4
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eor #$ff
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tax
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lda octant
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rol a
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and #%111
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tay
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lda atan_tab,x
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eor octant_adjust,y
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rts
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octant_adjust
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.byte %00111111 ;; x+,y+,|x|>|y|
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.byte %00000000 ;; x+,y+,|x|<|y|
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.byte %11000000 ;; x+,y-,|x|>|y|
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.byte %11111111 ;; x+,y-,|x|<|y|
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.byte %01000000 ;; x-,y+,|x|>|y|
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.byte %01111111 ;; x-,y+,|x|<|y|
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.byte %10111111 ;; x-,y-,|x|>|y|
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.byte %10000000 ;; x-,y-,|x|<|y|
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;;;;;;;; atan(2^(x/32))*128/pi ;;;;;;;;
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atan_tab
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.byte $00,$00,$00,$00,$00,$00,$00,$00
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.byte $00,$00,$00,$00,$00,$00,$00,$00
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.byte $00,$00,$00,$00,$00,$00,$00,$00
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.byte $00,$00,$00,$00,$00,$00,$00,$00
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.byte $00,$00,$00,$00,$00,$00,$00,$00
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.byte $00,$00,$00,$00,$00,$00,$00,$00
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.byte $00,$00,$00,$00,$00,$00,$00,$00
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.byte $00,$00,$00,$00,$00,$00,$00,$00
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.byte $00,$00,$00,$00,$00,$00,$00,$00
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.byte $00,$00,$00,$00,$00,$00,$00,$00
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.byte $00,$00,$00,$00,$00,$01,$01,$01
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.byte $01,$01,$01,$01,$01,$01,$01,$01
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.byte $01,$01,$01,$01,$01,$01,$01,$01
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.byte $01,$01,$01,$01,$01,$01,$01,$01
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.byte $01,$01,$01,$01,$01,$02,$02,$02
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.byte $02,$02,$02,$02,$02,$02,$02,$02
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.byte $02,$02,$02,$02,$02,$02,$02,$02
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.byte $03,$03,$03,$03,$03,$03,$03,$03
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.byte $03,$03,$03,$03,$03,$04,$04,$04
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.byte $04,$04,$04,$04,$04,$04,$04,$04
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.byte $05,$05,$05,$05,$05,$05,$05,$05
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.byte $06,$06,$06,$06,$06,$06,$06,$06
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.byte $07,$07,$07,$07,$07,$07,$08,$08
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.byte $08,$08,$08,$08,$09,$09,$09,$09
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.byte $09,$0a,$0a,$0a,$0a,$0b,$0b,$0b
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.byte $0b,$0c,$0c,$0c,$0c,$0d,$0d,$0d
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.byte $0d,$0e,$0e,$0e,$0e,$0f,$0f,$0f
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.byte $10,$10,$10,$11,$11,$11,$12,$12
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.byte $12,$13,$13,$13,$14,$14,$15,$15
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.byte $15,$16,$16,$17,$17,$17,$18,$18
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.byte $19,$19,$19,$1a,$1a,$1b,$1b,$1c
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.byte $1c,$1c,$1d,$1d,$1e,$1e,$1f,$1f
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;;;;;;;; log2(x)*32 ;;;;;;;;
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log2_tab
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.byte $00,$00,$20,$32,$40,$4a,$52,$59
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.byte $60,$65,$6a,$6e,$72,$76,$79,$7d
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.byte $80,$82,$85,$87,$8a,$8c,$8e,$90
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.byte $92,$94,$96,$98,$99,$9b,$9d,$9e
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.byte $a0,$a1,$a2,$a4,$a5,$a6,$a7,$a9
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.byte $aa,$ab,$ac,$ad,$ae,$af,$b0,$b1
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.byte $b2,$b3,$b4,$b5,$b6,$b7,$b8,$b9
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.byte $b9,$ba,$bb,$bc,$bd,$bd,$be,$bf
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.byte $c0,$c0,$c1,$c2,$c2,$c3,$c4,$c4
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.byte $c5,$c6,$c6,$c7,$c7,$c8,$c9,$c9
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.byte $ca,$ca,$cb,$cc,$cc,$cd,$cd,$ce
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.byte $ce,$cf,$cf,$d0,$d0,$d1,$d1,$d2
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.byte $d2,$d3,$d3,$d4,$d4,$d5,$d5,$d5
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.byte $d6,$d6,$d7,$d7,$d8,$d8,$d9,$d9
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.byte $d9,$da,$da,$db,$db,$db,$dc,$dc
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.byte $dd,$dd,$dd,$de,$de,$de,$df,$df
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.byte $df,$e0,$e0,$e1,$e1,$e1,$e2,$e2
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.byte $e2,$e3,$e3,$e3,$e4,$e4,$e4,$e5
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.byte $e5,$e5,$e6,$e6,$e6,$e7,$e7,$e7
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.byte $e7,$e8,$e8,$e8,$e9,$e9,$e9,$ea
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.byte $ea,$ea,$ea,$eb,$eb,$eb,$ec,$ec
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.byte $ec,$ec,$ed,$ed,$ed,$ed,$ee,$ee
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.byte $ee,$ee,$ef,$ef,$ef,$ef,$f0,$f0
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.byte $f0,$f1,$f1,$f1,$f1,$f1,$f2,$f2
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.byte $f2,$f2,$f3,$f3,$f3,$f3,$f4,$f4
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.byte $f4,$f4,$f5,$f5,$f5,$f5,$f5,$f6
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.byte $f6,$f6,$f6,$f7,$f7,$f7,$f7,$f7
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.byte $f8,$f8,$f8,$f8,$f9,$f9,$f9,$f9
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.byte $f9,$fa,$fa,$fa,$fa,$fa,$fb,$fb
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.byte $fb,$fb,$fb,$fc,$fc,$fc,$fc,$fc
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.byte $fd,$fd,$fd,$fd,$fd,$fd,$fe,$fe
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.byte $fe,$fe,$fe,$ff,$ff,$ff,$ff,$ff
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}}
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}
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}
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@ -182,4 +182,58 @@ math {
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return
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}}
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}
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sub atan_coarse_sgn(byte x1, byte y1, byte x2, byte y2) -> ubyte {
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; From a pair of signed coordinates around the origin, calculate discrete direction between 0 and 23 into A.
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cx16.r0L = 3 ; quadrant
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cx16.r1sL = x2-x1 ; xdelta
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if_neg {
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cx16.r0L--
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cx16.r1sL = -cx16.r1sL
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}
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cx16.r2sL = y2-y1 ; ydelta
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if_neg {
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cx16.r0L-=2
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cx16.r2sL = -cx16.r2sL
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}
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return atan_coarse_qd(cx16.r0L, cx16.r1L, cx16.r2L)
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}
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sub atan_coarse(ubyte x1, ubyte y1, ubyte x2, ubyte y2) -> ubyte {
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; From a pair of positive coordinates, calculate discrete direction between 0 and 23 into A.
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cx16.r0L = 3 ; quadrant
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if x2>=x1 {
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cx16.r1L = x2-x1
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} else {
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cx16.r1L = x1-x2
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cx16.r0L--
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}
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if y2>=y1 {
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cx16.r2L = y2-y1
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} else {
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cx16.r2L = y1-y2
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cx16.r0L -= 2
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}
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return atan_coarse_qd(cx16.r0L, cx16.r1L, cx16.r2L)
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}
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sub atan_coarse_qd(ubyte quadrant, ubyte xdelta, ubyte ydelta) -> ubyte {
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; From a pair of X/Y deltas (both >=0), and quadrant 0-3, calculate discrete direction between 0 and 23.
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return lsb(mkword(atan(0, 0, xdelta, ydelta), 0) / 2730)
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}
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sub atan(ubyte x1, ubyte y1, ubyte x2, ubyte y2) -> ubyte {
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;; Calculate the angle, in a 256-degree circle, between two points into A.
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;; The points (x1, y1) and (x2, y2) have to use *unsigned coordinates only* from the positive quadrant in the carthesian plane!
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%ir {{
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loadm.b r65532,math.atan.x1
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loadm.b r65533,math.atan.y1
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loadm.b r65534,math.atan.x2
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loadm.b r65535,math.atan.y2
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syscall 44 (r65532.b, r65533.b, r65534.b, r65535.b): r0.b
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returnr.b r0
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}}
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}
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}
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@ -372,6 +372,23 @@ but perhaps the provided ones can be of service too.
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Fast 8-bit byte cosine of angle 0..179 (each is a 2 degree step), result is in range -127..127
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Angles 180..255 will yield a garbage result!
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``atan(ubyte x1, ubyte y1, ubyte x2, ubyte y2)``
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Fast arctan routine that uses more memory because of large lookup tables.
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Calculate the angle, in a 256-degree circle, between two points in the positive quadrant.
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``atan_coarse_sgn(byte x1, byte y1, byte x2, byte y2)``
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Small and fast, but imprecise, arctan routine
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From a pair of signed coordinates around the origin, calculate discrete direction between 0 and 23.
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``atan_coarse(ubyte x1, ubyte y1, ubyte x2, ubyte y2)``
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Small and fast, but imprecise, arctan routine
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From a pair of positive coordinates, calculate discrete direction between 0 and 23.
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``atan_coarse_qd(ubyte quadrant, ubyte xdelta, ubyte ydelta)``
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Small and fast, but imprecise, arctan routine
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If you already know the quadrant and x/y deltas, calculate discrete direction between 0 and 23.
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cx16logo
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--------
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@ -1,6 +1,12 @@
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TODO
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====
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- this should give a compiler error because word returnvalue:
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sub atan_coarse_qd(ubyte quadrant, ubyte xdelta, ubyte ydelta) -> ubyte {
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return mkword(math.atan(0, 0, xdelta, ydelta), 0) / 2730
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}
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- vm: fix syscall.ATAN calculation
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- document some library modules better (diskio, etc)
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...
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@ -1,17 +1,44 @@
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%import math
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%import textio
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%import diskio
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%zeropage basicsafe
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main {
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sub start() {
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txt.print("pwd: ")
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txt.print(diskio.curdir())
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txt.print("\ndisk name: ")
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uword name = diskio.diskname()
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if name
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txt.print(name)
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else
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txt.print("!error!")
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const ubyte HEIGHT = 30 ; txt.DEFAULT_HEIGHT-1
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||||
const ubyte WIDTH = 80 ; txt.DEFAULT_WIDTH-1
|
||||
const ubyte HALFWIDTH = 40 ; txt.DEFAULT_WIDTH/2
|
||||
const ubyte HALFHEIGHT = 15 ; txt.DEFAULT_HEIGHT/2
|
||||
|
||||
txt.print_ub(math.atan(0, 0, 10, 20))
|
||||
|
||||
; ubyte @zp value
|
||||
; ubyte xx
|
||||
; ubyte yy
|
||||
; for yy in 0 to HEIGHT {
|
||||
; for xx in 0 to WIDTH {
|
||||
; value = math.atan(HALFWIDTH, HALFHEIGHT, xx, yy)
|
||||
; txt.setchr(xx,yy,value)
|
||||
; }
|
||||
; }
|
||||
;
|
||||
; byte sx
|
||||
; byte sy
|
||||
; for sy in 0 to HEIGHT as byte {
|
||||
; for sx in 0 to WIDTH as byte {
|
||||
; value = math.atan_coarse_sgn(0, 0, sx-HALFWIDTH, sy-HALFHEIGHT)
|
||||
; txt.setchr(sx as ubyte,sy as ubyte,value)
|
||||
; }
|
||||
; }
|
||||
;
|
||||
; for yy in 0 to HEIGHT {
|
||||
; for xx in 0 to WIDTH {
|
||||
; value = math.atan_coarse(HALFWIDTH, HALFHEIGHT, xx, yy)
|
||||
; txt.setchr(xx,yy,value)
|
||||
; }
|
||||
; }
|
||||
;
|
||||
; goto start
|
||||
}
|
||||
}
|
||||
|
|
|
|||
|
|
@ -42,6 +42,18 @@ SYSCALLS:
|
|||
30 = gfx_getpixel ; get byte pixel value at coordinates r0.w/r1.w
|
||||
31 = rndseed
|
||||
32 = rndfseed
|
||||
33 = RND
|
||||
34 = RNDW
|
||||
35 = RNDF
|
||||
36 = STRING_CONTAINS
|
||||
37 = BYTEARRAY_CONTAINS
|
||||
38 = WORDARRAY_CONTAINS
|
||||
39 = CLAMP_BYTE
|
||||
40 = CLAMP_UBYTE
|
||||
41 = CLAMP_WORD
|
||||
42 = CLAMP_UWORD
|
||||
43 = CLAMP_FLOAT
|
||||
43 = ATAN
|
||||
*/
|
||||
|
||||
enum class Syscall {
|
||||
|
|
@ -88,7 +100,8 @@ enum class Syscall {
|
|||
CLAMP_UBYTE,
|
||||
CLAMP_WORD,
|
||||
CLAMP_UWORD,
|
||||
CLAMP_FLOAT
|
||||
CLAMP_FLOAT,
|
||||
ATAN
|
||||
;
|
||||
|
||||
companion object {
|
||||
|
|
@ -454,12 +467,25 @@ object SysCalls {
|
|||
}
|
||||
Syscall.CLAMP_FLOAT -> {
|
||||
val (valueU, minimumU, maximumU) = getArgValues(callspec.arguments, vm)
|
||||
val value = (valueU as Float)
|
||||
val minimum = (minimumU as Float)
|
||||
val maximum = (maximumU as Float)
|
||||
val value = valueU as Float
|
||||
val minimum = minimumU as Float
|
||||
val maximum = maximumU as Float
|
||||
val result = min(max(value, minimum), maximum)
|
||||
returnValue(callspec.returns!!, result, vm)
|
||||
}
|
||||
Syscall.ATAN -> {
|
||||
val (x1, y1, x2, y2) = getArgValues(callspec.arguments, vm)
|
||||
val x1f = (x1 as UByte).toDouble()
|
||||
val y1f = (y1 as UByte).toDouble()
|
||||
val x2f = (x2 as UByte).toDouble()
|
||||
val y2f = (y2 as UByte).toDouble()
|
||||
val xd = x2f-x1f
|
||||
val yd = y2f-y1f
|
||||
TODO("calculate atan the same way as the 6502 routine does 0-255")
|
||||
// val radians = atan2(yd, xd) + PI // 0 to 2*PI
|
||||
// val result = floor(2*PI/radians*256.0)
|
||||
// returnValue(callspec.returns!!, result, vm)
|
||||
}
|
||||
else -> throw AssemblyError("missing syscall ${call.name}")
|
||||
}
|
||||
}
|
||||
|
|
|
|||
Loading…
Reference in New Issue
Block a user